Dubins-Curves

About

This software finds the shortest paths between configurations for the Dubins' car [Dubins51], the forward only car-like vehicle with a constrained turning radius. A good description of the equations and basic strategies for doing this are described in section 15.3.1 "Dubins Curves" of the book "Planning Algorithms" [LaValle06].

Demo

The approach used to find paths is based on the algebraic solutions published in [Shkel01]. However, rather than using angular symmetries to improve performance, the simpler approach to test all possible solutions is used here.

Usage

The recommended approach is to add dubins.c and dubins.h to your project and compile with an appropriate build system.

The repository includes a basic cmake example that demonstrates how to build and test the library.

Examples

The following code animates ball from [0,0] with direction Math.Pi to point B [100, 100, -Math.Pi], along the shortest path.

let start = null
let ball = document.querySelector('#ball');

/* Arguments: [x0,y1,angle0], [x1,y1,angle1], radius */
let path = DubinsAPI.init( [0,   0,    Math.Pi], 
                        [200, 200, -Math.Pi], 50 );

/*
* Interpolate from 0 to path.length
*/
function animate( time ){
    if(!start) start = time

    // Sample position at current time
    let t = (time - start)/1000
    let [mx,my,angle] = DubinsAPI.sample( path , t )

    // Animate using CSS Transforms for better performance
    let transRot  = `rotate(${angle.toFixed(2)}rad)`
    let transPos  = `translate(${mx.toFixed(2)}px, ${my.toFixed(2)}px)`
    let transform = `${transPos} ${transRot}`

    ball.style.transform = transform 
    ball.style.webkitTransform = transform

    if(t < path.length){
        requestAnimationFrame(animate)
    }
}
requestAnimationFrame(animate)

The following image shows some example paths, and the heading of the vehicle at each of the intermediate configurations.

Other Version

• There is a MATLAB Mex wrapper of this code on the MathWorks FileExchange
• There is a Python wrapper of this code available on GitHub and on PyPI

Citing

If you would like to cite this library in a paper or presentation, the following is recommended:

@Misc{DubinsCurves,
  author = {Andrew Walker},
  title  = {Dubins-Curves: an open implementation of shortest paths for the forward only car},
  year   = {2008--},
  url    = "https://github.com/AndrewWalker/Dubins-Curves"
}

Contributors

The Dubin's curves library was completed as one small part of [Walker11]. New contributions or bug fixes are welcome.

Key contributors to the project include:

• Francis Valentinis
• Royce Smart - who tested early versions of this code while writing up [Smart08].
• Scott Teuscher - who wrote the MATLAB Mex wrapper

License

MIT License. See LICENSE.txt for details.

References

Dubins51

Dubins, L.E. (July 1957). "On Curves of Minimal Length with a Constraint on Average Curvature, and with Prescribed Initial and Terminal Positions and Tangents". American Journal of Mathematics 79 (3): 497–516

LaValle06

LaValle, S. M. (2006). "Planning Algorithms". Cambridge University Press

Shkel01

Shkel, A. M. and Lumelsky, V. (2001). "Classification of the Dubins set". Robotics and Autonomous Systems 34 (2001) 179–202

Smart08

Royce, S. (2008). "Evolutionary Control of Autonomous Underwater Vehicles". PhD thesis, RMIT

Walker11

Walker, A. (2011). "Hard Real-Time Motion Planning for Autonomous Vehicles", PhD thesis, Swinburne University.